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janhardo

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@nm  simplify(int(sqrt(1 + sin(x)...

janhardo 840
December 27 2025
0 0

@nm 

simplify(int(sqrt(1 + sin(x)^2), x), symbolic);

and this ?
 

int(sqrt(1 + sin(x)^2), x, method=_RETURNVERBOSE);

A left Riemann sum for sin(x)  ...

janhardo 840
December 23 2025
0 0

A left Riemann sum for sin(x) 

"maple.ini in user"

 (1)
> 

NULL

 

 
> 

restart:
with(Student:-Calculus1):

RiemannSum(
    sin(x),
    x = 0...2*Pi,
    partition = 50,
    method = left,
    output = plot, size=[1000,600]
);

"maple.ini in user"

 

 
> 

Int(sin(x), x = 0..2*Pi) = int(sin(x), x = 0..2*Pi);

Int(sin(x), x = 0 .. 2*Pi) = 0

(1.1)
> 

Limit(Sum(sin(2*Pi*i/n)*(2*Pi/n), i=1..n), n=infinity)= limit(sum(sin(2*Pi*i/n)*(2*Pi/n), i=1..n), n=infinity); # a limit of sums

Limit(Sum(2*sin(2*Pi*i/n)*Pi/n, i = 1 .. n), n = infinity) = 0

(1.2)
> 

Int(sin(x), x = 0 .. 2*Pi) =  Limit(Sum(2*sin(2*Pi*i/n)*Pi/n, i = 1 .. n), n = infinity) ;

Int(sin(x), x = 0 .. 2*Pi) = Limit(Sum(2*sin(2*Pi*i/n)*Pi/n, i = 1 .. n), n = infinity)

(1.3)
> 

verify(
  int(sin(x), x = 0 .. 2*Pi),
  limit(sum(2*sin(2*Pi*i/n)*Pi/n, i = 1 .. n), n = infinity),
  equal
);

true

(1.4)
 

NULL

Download linker_riemannsom_voor_sinus_plot_mprimes_23-12-2025.mw

dimensions in  A en B    ...

janhardo 840
December 23 2025
0 0

dimensions in  A en B    are not possible ?

A := Vector(2, symbol=a):
B := Matrix(2$2, symbol=b):
R := A.B.A^+

  > ....

janhardo 840
December 23 2025
0 0


 

> 

NULL

 

 
> 

NULL

> 

restart;

RiemannPlot := proc({meth::string:="left", n::posint:=5, animate::boolean:=false})
    local f, a, b, dx, xvals, yvals, i, exact, approx, k,
          plot_func, rect_plots, point_plots, line_plots, rect_color,
          frames, frame_list, anim, left_x, right_x, rect_height;
    
    f := x -> x^2;
    a := 0;
    b := 1;
    exact := 1/3;  # ∫₀¹ x² dx = 1/3
    
    # If animation is requested, create a series of frames
    if animate then
        frames := [seq(i, i=2..20, 2)];  # n = 2, 4, 6, ..., 20
        frame_list := [];
        
        for k in frames do
            dx := (b - a)/k;
            
            # Generate x-values based on the method
            if meth = "left" then
                xvals := [seq(a + (i-1)*dx, i = 1..k)];
                rect_color := "LightBlue";
            elif meth = "right" then
                xvals := [seq(a + i*dx, i = 1..k)];
                rect_color := "LightGreen";
            elif meth = "midpoint" then
                xvals := [seq(a + (i-1/2)*dx, i = 1..k)];
                rect_color := "LightPink";
            else
                error "Invalid method. Choose 'left', 'right' or 'midpoint'";
            end if;
            
            yvals := map(f, xvals);
            approx := add(yvals[i]*dx, i = 1..k);
            
            # Create rectangles with smart borders
            rect_plots := NULL;
            for i from 1 to k do
                left_x := a + (i-1)*dx;
                right_x := a + i*dx;
                rect_height := yvals[i];
                
                # Colored rectangle
                rect_plots := rect_plots,
                    plottools:-rectangle([left_x, 0], [right_x, rect_height],
                                         color = rect_color, style = polygon,
                                         transparency = 0.3);
                
                # Draw rectangle borders intelligently
                if rect_height > 0 then
                    if meth = "left" then
                        # ALWAYS draw bottom
                        rect_plots := rect_plots,
                            plot([[left_x, 0], [right_x, 0]],
                                 color = "Black", thickness = 0.5);
                        
                        # ALWAYS draw top
                        rect_plots := rect_plots,
                            plot([[left_x, rect_height], [right_x, rect_height]],
                                 color = "Black", thickness = 0.5);
                        
                        # Draw LEFT side ONLY for FIRST rectangle
                        if i = 1 then
                            rect_plots := rect_plots,
                                plot([[left_x, 0], [left_x, rect_height]],
                                     color = "Black", thickness = 0.5);
                        end if;
                        
                        # Draw RIGHT side ONLY for LAST rectangle
                        if i = k then
                            rect_plots := rect_plots,
                                plot([[right_x, 0], [right_x, rect_height]],
                                     color = "Black", thickness = 0.5);
                        end if;
                        
                    elif meth = "right" then
                        # ALWAYS draw bottom
                        rect_plots := rect_plots,
                            plot([[left_x, 0], [right_x, 0]],
                                 color = "Black", thickness = 0.5);
                        
                        # ALWAYS draw top
                        rect_plots := rect_plots,
                            plot([[left_x, rect_height], [right_x, rect_height]],
                                 color = "Black", thickness = 0.5);
                        
                        # Draw LEFT side (always for right method)
                        rect_plots := rect_plots,
                            plot([[left_x, 0], [left_x, rect_height]],
                                 color = "Black", thickness = 0.5);
                        
                        # Draw RIGHT side ONLY for LAST rectangle
                        if i = k then
                            rect_plots := rect_plots,
                                plot([[right_x, 0], [right_x, rect_height]],
                                     color = "Black", thickness = 0.5);
                        end if;
                        
                    else  # midpoint
                        # Draw ALL sides (dashed line is in middle, no overlap)
                        rect_plots := rect_plots,
                            plot([[left_x, 0], [right_x, 0]],  # Bottom
                                 color = "Black", thickness = 0.5);
                        rect_plots := rect_plots,
                            plot([[left_x, 0], [left_x, rect_height]],  # Left
                                 color = "Black", thickness = 0.5);
                        rect_plots := rect_plots,
                            plot([[right_x, 0], [right_x, rect_height]],  # Right
                                 color = "Black", thickness = 0.5);
                        rect_plots := rect_plots,
                            plot([[left_x, rect_height], [right_x, rect_height]],  # Top
                                 color = "Black", thickness = 0.5);
                    end if;
                end if;
            end do;
            
            # Points and vertical dashed lines
            point_plots := NULL;
            line_plots := NULL;
            for i from 1 to k do
                if yvals[i] > 0 then
                    point_plots := point_plots,
                        plot([[xvals[i], yvals[i]]], style = point, symbol = solidcircle,
                             symbolsize = 10, color = "Red");
                    
                    # Vertical dashed line
                    line_plots := line_plots,
                        plot([[xvals[i], 0], [xvals[i], yvals[i]]],
                             color = "Red", linestyle = dash, thickness = 0.5);
                end if;
            end do;
            
            # Function curve
            plot_func := plot(f(x), x = a..b, color = "DarkBlue", thickness = 2);
            
            # Add frame to list
            frame_list := [op(frame_list),
                plots:-display([rect_plots, line_plots, plot_func, point_plots],
                              title = sprintf("Riemann Sum (%s) for f(x) = x²\nn = %d | Approximation: %.5f | Exact: %.5f",
                                             meth, k, approx, exact),
                              view = [a..b, -0.1..1.1],
                              axes = boxed,
                              labels = ["x", "f(x)"])];
        end do;
        
        # Create the animation
        anim := plots:-display(frame_list, insequence = true);
        return anim;
        
    else
        # Static plot
        dx := (b - a)/n;
        
        # Generate x-values based on the method
        if meth = "left" then
            xvals := [seq(a + (i-1)*dx, i = 1..n)];
            rect_color := "LightBlue";
        elif meth = "right" then
            xvals := [seq(a + i*dx, i = 1..n)];
            rect_color := "LightGreen";
        elif meth = "midpoint" then
            xvals := [seq(a + (i-1/2)*dx, i = 1..n)];
            rect_color := "LightPink";
        else
            error "Invalid method. Choose 'left', 'right' or 'midpoint'";
        end if;
        
        yvals := map(f, xvals);
        approx := add(yvals[i]*dx, i = 1..n);
        
        # Create rectangles with smart borders
        rect_plots := NULL;
        for i from 1 to n do
            left_x := a + (i-1)*dx;
            right_x := a + i*dx;
            rect_height := yvals[i];
            
            # Colored rectangle
            rect_plots := rect_plots,
                plottools:-rectangle([left_x, 0], [right_x, rect_height],
                                     color = rect_color, style = polygon,
                                     transparency = 0.3);
            
            # Draw rectangle borders intelligently
            if rect_height > 0 then
                if meth = "left" then
                    # ALWAYS draw bottom
                    rect_plots := rect_plots,
                        plot([[left_x, 0], [right_x, 0]],
                             color = "Black", thickness = 1);
                    
                    # ALWAYS draw top
                    rect_plots := rect_plots,
                        plot([[left_x, rect_height], [right_x, rect_height]],
                             color = "Black", thickness = 1);
                    
                    # Draw LEFT side ONLY for FIRST rectangle
                    if i = 1 then
                        rect_plots := rect_plots,
                            plot([[left_x, 0], [left_x, rect_height]],
                                 color = "Black", thickness = 1);
                    end if;
                    
                    # Draw RIGHT side ONLY for LAST rectangle
                    if i = n then
                        rect_plots := rect_plots,
                            plot([[right_x, 0], [right_x, rect_height]],
                                 color = "Black", thickness = 1);
                    end if;
                    
                elif meth = "right" then
                    # ALWAYS draw bottom
                    rect_plots := rect_plots,
                        plot([[left_x, 0], [right_x, 0]],
                             color = "Black", thickness = 1);
                    
                    # ALWAYS draw top
                    rect_plots := rect_plots,
                        plot([[left_x, rect_height], [right_x, rect_height]],
                             color = "Black", thickness = 1);
                    
                    # Draw LEFT side (always for right method)
                    rect_plots := rect_plots,
                        plot([[left_x, 0], [left_x, rect_height]],
                             color = "Black", thickness = 1);
                    
                    # Draw RIGHT side ONLY for LAST rectangle
                    if i = n then
                        rect_plots := rect_plots,
                            plot([[right_x, 0], [right_x, rect_height]],
                                 color = "Black", thickness = 1);
                    end if;
                    
                else  # midpoint
                    # Draw ALL sides (dashed line is in middle, no overlap)
                    rect_plots := rect_plots,
                        plot([[left_x, 0], [right_x, 0]],  # Bottom
                             color = "Black", thickness = 1);
                    rect_plots := rect_plots,
                        plot([[left_x, 0], [left_x, rect_height]],  # Left
                             color = "Black", thickness = 1);
                    rect_plots := rect_plots,
                        plot([[right_x, 0], [right_x, rect_height]],  # Right
                             color = "Black", thickness = 1);
                    rect_plots := rect_plots,
                        plot([[left_x, rect_height], [right_x, rect_height]],  # Top
                             color = "Black", thickness = 1);
                end if;
            end if;
        end do;
        
        # Points and vertical dashed lines
        point_plots := NULL;
        line_plots := NULL;
        for i from 1 to n do
            if yvals[i] > 0 then
                point_plots := point_plots,
                    plot([[xvals[i], yvals[i]]], style = point, symbol = solidcircle,
                         symbolsize = 12, color = "Red");
                
                # Vertical dashed line
                line_plots := line_plots,
                    plot([[xvals[i], 0], [xvals[i], yvals[i]]],
                         color = "Red", linestyle = dash, thickness = 1);
            end if;
        end do;
        
        # Function curve
        plot_func := plot(f(x), x = a..b, color = "DarkBlue", thickness = 2);
        
        # Display the plot
        return plots:-display([rect_plots, line_plots, plot_func, point_plots],
                             title = sprintf("Riemann Sum (%s) for f(x) = x² with n = %d\nExact: %.5f | Approximation: %.5f | Error: %.5f",
                                            meth, n, exact, approx, abs(exact-approx)),
                             view = [a..b, -0.1..1.1],
                             axes = boxed,
                             labels = ["x", "f(x)"]);
    end if;
end proc:

"maple.ini in user"

(1.1)
> 

NULL

> 

# ========== DRIE STATISCHE PLOTS ==========
print("=== THREE STATIC PLOTS ===");

# 1. Left endpoint method
p1 := RiemannPlot(meth = "left", n = 8):
print("Left endpoint plot created");
p1;

# 2. Midpoint method  
p2 := RiemannPlot(meth = "midpoint", n = 8):
print("Midpoint plot created");
p2;

# 3. Right endpoint method
p3 := RiemannPlot(meth = "right", n = 8):
print("Right endpoint plot created");
p3;

# Display all three static plots side by side
with(plots):
print("=== DISPLAYING ALL THREE STATIC PLOTS ===");
display(Array([p1, p2, p3]), title = "Comparison of Riemann Sum Methods (n=8)", size = [1200, 400]);

# ========== DRIE ANIMATIES ==========
print("=== CREATING THREE ANIMATIONS ===");

# 1. Animation for left endpoint method
print("Creating left endpoint animation...");
anim1 := RiemannPlot(meth = "left", animate = true):
print("Left endpoint animation created");

# 2. Animation for midpoint method  
print("Creating midpoint animation...");
anim2 := RiemannPlot(meth = "midpoint", animate = true):
print("Midpoint animation created");

# 3. Animation for right endpoint method
print("Creating right endpoint animation...");
anim3 := RiemannPlot(meth = "right", animate = true):
print("Right endpoint animation created");

# Display all three animations
print("=== DISPLAYING ALL THREE ANIMATIONS ===");

# Option 1: Display animations one after another
print("Animation 1: Left Endpoint Method");
anim1;

print("Animation 2: Midpoint Method");
anim2;

print("Animation 3: Right Endpoint Method");
anim3;

# Option 2: Display animations in an array (might not work for animations in all Maple versions)
# display(Array([anim1, anim2, anim3]), title = "Comparison of Riemann Sum Animations");

"=== THREE STATIC PLOTS ==="

 

"Left endpoint plot created"

 

 

"Midpoint plot created"

 

 

"Right endpoint plot created"

 

 

"=== DISPLAYING ALL THREE STATIC PLOTS ==="

 

 

 
 

 

 

  

"=== CREATING THREE ANIMATIONS ==="

 

"Creating left endpoint animation..."

 

"Left endpoint animation created"

 

"Creating midpoint animation..."

 

"Midpoint animation created"

 

"Creating right endpoint animation..."

 

"Right endpoint animation created"

 

"=== DISPLAYING ALL THREE ANIMATIONS ==="

 

"Animation 1: Left Endpoint Method"

 

 

"Animation 2: Midpoint Method"

 

 

"Animation 3: Right Endpoint Method"

 

 
> 

 

> 

NULL


 

Download Riemann_someemn_mprimes_23-12-2025.mw

@salim-barzani  You need the math f...

janhardo 840
December 22 2025
0 0

@salim-barzani 
You need the math for doing this ...

@dharr Your code is invaluable, and...

janhardo 840
December 21 2025
0 0

@dharr Your code is invaluable, and I don't know if the ai is clever enough if it gets the problem definition for this , to come up with the right programming too ?
The ideas in  your code are a basis for variants via AI.

variants_op_maple_collect_21-12-2025.mw

@dharr , this should work now ...

janhardo 840
December 19 2025
0 0

@dharr , this should work now 

Download corr_-def_proc_rangschikking_polynoom_8-12-2025_19-12-2025.mw

@salim-barzani  Perhaps the AI will...

janhardo 840
December 15 2025
0 0

@salim-barzani 
Perhaps the AI will come up with a suitable solution, otherwise I don't know either
.generalisatie_Bij_mprimes_vraag_15-12-2025.mw

@salim-barzani  restart;# Shor...

janhardo 840
December 15 2025
0 0

@salim-barzani 

restart;

# Shorter version
e_ij := ((3*c1*ki*(ki - kj)*lj - c3)*li^2 - 3*(c1*kj*(ki - kj)*lj - (2/3)*c3)*lj*li - c3*lj^2) /
        ((3*c1*ki*(ki + kj)*lj - c3)*li^2 + 3*(c1*kj*(ki + kj)*lj + (2/3)*c3)*lj*li - c3*lj^2);

# Show the limit definition using the inert form
Limit_definition := Limit((subs(ki=k1, kj=k3, li=l1, lj=l3, e_ij) - 1)/(k1*k3), k1=0)= limit((subs(ki=k1, kj=k3, li=l1, lj=l3, e_ij) - 1)/(k1*k3), k1=0);

# Calculate the limit using the active form
B13_direct := limit((subs(ki=k1, kj=k3, li=l1, lj=l3, e_ij) - 1)/(k1*k3), k1=0);

# Simplify
B13_result := simplify(B13_direct);

@salim-barzani  Dr.D_thanks_mijn_co...

janhardo 840
December 13 2025
0 0

@salim-barzani 
Dr.D_thanks_mijn_correctie_omwerkend_t_ekrijgen_13-12-2025.mw

partieke_afgeleide_in_bewijs_oplossing_v...

janhardo 840
December 13 2025
0 0

partieke_afgeleide_in_bewijs_oplossing_van_ode_13-12-2025.mw 

@dharr  I did that deliberatel...

janhardo 840
December 11 2025
0 0

@dharr  I did that deliberately by giving your code approach to the AI, which will then do something with it.

It could just as easily give another code approach that the AI devises as a solution to this task, but that might be more difficult to follow, yet work better?

It would also be interesting to ask the AI for a variant on your code, and the programming would probably remain closer to the original programming?
Testing with this simple example is a serious error, yes.

@nm I did this and it works for me....

janhardo 840
December 11 2025
0 0

@nm 
I did this and it works for me.
The URL that this page gives on Maple Primes is displayed in the browser.

Here is an example: https://www.mapleprimes.com/questions/242066-Unable-To-Upload-WorkshEXAMPLE

Remove the part of the URL: /questions/242066-Unable-To-Upload-WorkshEXAMPLE so that you get https://www.mapleprimes.com again.
I make a new link too by copy the url  

Nothing to worry about. I got the same t...

janhardo 840
December 10 2025
0 0

Nothing to worry about. I got the same thing today and the solution is to use again: https://www.mapleprimes.com

def_proc_rangschikking_polynoom_8-12-202...

janhardo 840
December 09 2025
0 0

def_proc_rangschikking_polynoom_8-12-2025.mw

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